How to correctly drive a normal node with lamp rotation?
This is a bit tricky, since the value range of the normal vector is (-1, 1). But you appears to control it by object rotation, which circle range is from 0° to 360°. It doesn't make any sense to add drivers between them.

You can use Mapping node to control the Normal vector output, driven by the object rotation (in degrees or radians). However, Blender internally uses Radians instead of Degrees, that's why you'll see the driver value shows in both radian and degree system.

So, you need to do some radian calculation for the driver expression. In this case, on the newly added Normal node (with the "control ball"  UNTOUCHED), you need to add/subtract a half circle for it, which equals pi.



Example file: